Particle beam radiotherapy delivers charged particles to a tumor while minimizing damage to surrounding healthy tissue. An energy deposition profile of the particles has a Bragg peak. The peak occurs immediately before the particles come to rest. The profile can be controlled to deliver a maximum energy within a few millimeters of the range of the particles. Thus, the prescribed irradiation is focused on the tumor with little side scatter and broadening of the beam.
However, due to random and systemic motion, the tumor must be tracked continuously in real-time during treatment. Several modalities such as ultrasound, X-ray, and magnetic resonance imaging (MRI), are used to track internal structures of the body. Among these, the ultrasound imaging offers a noninvasive alternative to X-ray. Being cost and time efficient, a high-frequency ultrasound system with 3-D imaging capabilities also achieves better resolution, discrimination and detection of abdominal metastases at a minimum size, and compares favorably with that of X-ray imaging.
Ultrasound imaging depicts not only the center of the tumor but also the entire volume and boundary for a large variety of high contrast neoplasms. Ultrasound imaging is conventionally used for detection and staging of tumors
For visible tumors, the tumor tracking can be performed by image segmentation, wherein each pixel is labeled either as foreground (tumor), or background (healthy tissue). This task fits naturally into level set and graph partitioning techniques. For image segmentation, the level set describes the evolution of a front over time, and more specifically for image segmentation, a boundary between two separate and closed regions.
By indirectly modeling the front as an embedding of a zero level set of an implicit time-dependent higher dimensional function, these challenges are addressed without the need to treat them as special cases. Then, the evolving front can be followed by tracking the zero level set of that implicit function, for example, starting with a closed curve and allowing the curve to move perpendicularly to itself from an initial speed, derived locally from an image. Typical techniques represent the evaluation of the curve by a discrete parameterization as a set of points whose locations are updated according to a given model.
Graph cut based segmentation techniques are efficient, accurate, and guarantee a global optimum for a wide family of energy functionals. In graph theory, a cut is a partition of the vertices (nodes) of a graph into two disjoint subsets. Given a set of foreground pixels and a set of background pixels, an image is represented by a graph, and a maximum a posteriori (MAP) estimate of a binary segmentation can be obtained by maximizing the flow through the graph. Evaluated for an object/background assignment, the graph edge energies are designed as a data dependent term. Each pixel is considered as a vertex in the graph.
The graph includes two additional vertices, a source and a sink, which represent the overall foreground and background, respectively. A data dependent term is realized by connecting each pixel in an image to both the object and background vertices with weighted edges. A minimum cut of the weighted graph represents the segmentation that best separates the foreground from the background. A cut is minimal if the sum of the weights along the cut is not larger than the sum of any other cut. Due to this property, graph cut methods tend to generate compact regions, even if the underlying appearance depicts elongated objects.
Shape prior information can be incorporated in the graph cut framework without compromising the global optimality of the process. The shape prior information can be encoded using a distance transform of the shape after the prior information and images are aligned at multiple scales and a pair-wise cost term is appended with a shape match cost term for neighboring pixels. This cost term is submodular. Hence, the global optimal solution can still be obtained. However, the modified process has to be repeated for different scales to determine the best match, which is time consuming.
Other techniques incorporate shape prior information into unary terms. Kernel principal component analysis (PCA) can be used to train a generative model from training shapes. Graph cuts are performed iteratively starting with an initial contour. During each iteration, a pre-image is generated from the trained shape model, based on the segmentation from the previous iteration. The pre-image is used as a prior probability map, and a pixel-wise negative log-likelihood value is used to modify the terminal weights coded by the unary terms. An image normalization process is utilized to handle affine transformation of the shapes. By posing the multiphase level set segmentation in the graph cut framework, the method can segment disconnected regions.
One method is for tracking the left ventricle in 3D ultrasound images. However, that method is highly complex and relies on supervised learning on a training dataset, which may not be available in all cases.
Most graph cut methods are highly sensitive to the location and number of the source and sink pixels. A multi-label segmentation is posed as a random walk problem. An equivalent continuous Dirichlet process is reformulated on a graph using the combinatorial operators. Image segmentation is obtained by solving a sparse system of linear equations constrained on the given labels of a set of seed pixels (seeds). Color prior probability information, in the form of a Gaussian mixture obtained from training data, can be incorporated into the random walk segmentation process.
However, extending the above described methods to tracking tumor in a sequence of images is not straightforward and requires an elaborate or manual selection of the sink and source pixels in consecutive images.